Multiple choice

DIRECTION for the question: Solve the following question and mark the best possible option. A can contains a mixture of liquids, A and B in ratio 7:5. when 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres A was conatined by the can initially?

  1. 22

  2. 21

  3. 27

  4. 50

  5. 35
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A = 7x, B = 5x. Total = 12x. After drawing 9L, A = 7x - 7/12 * 9 = 7x - 5.25. B = 5x - 5/12 * 9 = 5x - 3.75. Adding 9L of B: B = 5x - 3.75 + 9 = 5x + 5.25. Ratio (7x - 5.25) / (5x + 5.25) = 7/9. 63x - 47.25 = 35x + 36.75. 28x = 84. x = 3. Initial A = 7 * 3 = 21.

AI explanation

Let the initial volume of liquid A and liquid B be 7x and 5x. When 9 liters of the mixture is removed, 7/12 of 9 liters of liquid A is removed, leaving 7x minus 5.25 liters of A, and 5x minus 3.75 liters of B. Adding 9 liters of liquid B changes the ratio to 7:9, giving the equation (7x minus 5.25) divided by (5x plus 5.25) equals 7 divided by 9. Solving this yields 63x minus 47.25 equals 35x plus 36.75, meaning 28x equals 84, so x equals 3. The initial amount of liquid A was 7x, resulting in 21 liters.

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